Quantile, equal interval, and natural breaks methods are widely used data classification methods in geospatial analysis and cartography. However, when applied to data with skewed distributions, they can only reveal the variations of either high frequent values or extremes, which often leads to undesired and biased classification results. To handle this problem, Esri provided a compromise method, named geometric interval classification (GIC). Although GIC performs well for various classification tasks, its mathematics and solution process remain unclear. Moreover, GIC is theoretically only applicable to single-peak (single-modal), one-dimensional data. This paper first mathematically formulates GIC as a general optimization problem subject to equality constraint. We then further adapt such formulated GIC to handle multi-peak and multi-dimensional data. Both thematic data and remote sensing images are used in this study. The comparison with other classification methods demonstrates the advantage of GIC being able to highlight both middle and extreme values. As such, it can be regarded as a general data classification approach for thematic mapping and other geospatial applications.

Urban visual localization is the process of determining the pose (position and attitude) of the imaging sensor (or platform) with the help of existing geo-referenced data. This task is critical and challenging for many applications, such as autonomous navigation, virtual and augmented reality, and robotics, due to the dynamic and complex nature of urban environments that may obstruct Global Navigation Satellite Systems (GNSS) signals. This paper proposes a block-wise matching strategy for urban visual localization by using geo-referenced Google Street View (GSV) panoramas as the database. To determine the pose of the monocular query images collected from a moving vehicle, neighboring GSVs should be found to establish the correspondence through image-wise and block-wise matching. First, each query image is semantically segmented and a template containing all permanent objects is generated. The template is then utilized in conjunction with a template matching approach to identify the corresponding patch from each GSV image within the database. Through the conversion of the query template and corresponding GSV patch into feature vectors, their image-wise similarity is computed pairwise. To ensure reliable matching, the query images are temporally grouped into query blocks, while the GSV images are spatially organized into GSV blocks. By using the previously computed image-wise similarities, we calculate a block-wise similarity for each query block with respect to every GSV block. A query block and its corresponding GSV blocks of top-ranked similarities are then input into a photogrammetric triangulation or structure from motion process to determine the pose of every image in the query block. A total of three datasets, consisting of two public ones and one newly collected on the Purdue campus, are utilized to demonstrate the performance of the proposed method. It is shown it can achieve a meter-level positioning accuracy and is robust to changes in acquisition conditions, such as image resolution, scene complexity, and the time of day.

Estimation of image or camera pose, including three position and three rotation parameters, is a fundamental task in remote sensing. When GNSS signal is not available or interfered, accurate pose estimation is still challenging since its initials can be rather rough and the search space is large. Conventional solutions to such problems rely on ground control points that are identifiable in the images. However, this is an unrealistic or inconvenient requirement for many applications. We report a novel approach that uses a 3D road database to determine the image pose without known image-road correspondence. After the road database is projected to images using current estimated pose, we calculate a set of spectral and geometric road attributes for these projections. Taking advantage of the geometry of an image triplet, road projections from two neighboring images are transferred to the third one. For each image triplet, the final estimated pose minimizes the differences among the attributes of the road projections, extracted image roads and transferred roads. Tests using two drone image datasets demonstrate that this approach can obtain accurate pose at an uncertainty less than 2.2 m and 2.6° compared to the bundle adjustment results. The use of image triplet considerably improves the robustness and accuracy of independent single image pose estimation. The developed visual hull quality metric can intrinsically determine the reliability of the estimated pose. This work will benefit image-based positioning and mapping applications where images have no ground control points or GNSS signals are degraded.